Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
Correct Answer
$6996
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5300 × 4% × 8
= $5300 ×4/100 × 8
= 5300 × 4 × 8/100
= 21200 × 8/100
= 169600/100
= $1696
Thus, Simple Interest = $1696
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1696
= $6996
Thus, Amount to be paid = $6996 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5300
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 4% × 8)
= $5300 + ($5300 ×4/100 × 8)
= $5300 + (5300 × 4 × 8/100)
= $5300 + (21200 × 8/100)
= $5300 + (169600/100)
= $5300 + $1696 = $6996
Thus, Amount (A) to be paid = $6996 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5300, the simple interest in 1 year
= 4/100 × 5300
= 4 × 5300/100
= 21200/100 = $212
Thus, simple interest for 1 year = $212
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $212 × 8 = $1696
Thus, Simple Interest (SI) = $1696
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1696
= $6996
Thus, Amount to be paid = $6996 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(3) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(6) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.
(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.